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Exceptional Prime Number Twins, Triplets and Multiplets [PDF]

arXiv, 2011
A classification of twin primes implies special twin primes. When applied to triplets, it yields exceptional prime number triplets. These generalize yielding exceptional prime number multiplets.
arxiv  

Goldbach's Problem in Primes with Binary Expansions of a Special Form [PDF]

arXiv, 2012
Let $\mathbb{N}_0$ be a class of natural numbers whose binary expansions contain even numbers of ones. Goldbach's problem in numbers of class $\mathbb{N}_0$ is solved.
arxiv